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Table 10 Longitudinal measurement invariance for STMS models following Geiser et al. (2015)

From: Psychological determinants of test motivation in low-stakes test situations: A longitudinal study of singletrait–multistate models in accounting

Model

N

Par

χ2

df

χ2/df

CFI

TLI

RMSEA

SRMR

LLCorFac

TRd*

TRd p*

∆CFI*

∆RMSEA*

VALUE

M1: no measurement invariance (mi)

486

56

48.99

34

1.44

0.985

0.971

0.030

0.037

1.467

    

M2: trait loading mi

486

50

52.82

40

1.32

0.987

0.979

0.026

0.046

1.424

2.83

0.83

0.002

− 0.004

M3: trait loading and intercept mi

486

44

68.95

46

1.50

0.977

0.968

0.032

0.054

1.422

16.21

0.01

− 0.010

0.006

M4: trait loading. intercept and state loading mi

486

38

80.64

52

1.55

0.972

0.964

0.034

0.058

1.441

11.44

0.08

− 0.005

0.002

EFFOR

M1: no measurement invariance (mi)

486

86

199.83

103

1.94

0.959

0.939

0.044

0.054

1.306

    

M2: trait loading mi

486

76

204.80

113

1.81

0.961

0.947

0.041

0.062

1.295

3.64

0.96

0.002

− 0.003

M3: trait loading and intercept mi

486

66

217.29

123

1.77

0.960

0.950

0.040

0.066

1.279

11.52

0.32

− 0.001

− 0.001

M4: trait loading. intercept and state loading mi

486

56

259.26

133

1.95

0.946

0.938

0.044

0.060

1.365

31.31

0.00

− 0.014

0.004

INTRI

M1: no measurement invariance (mi)

612

71

139.92

64

2.19

0.982

0.970

0.044

0.038

1.433

    

M2: trait loading mi

612

63

145.37

72

2.02

0.982

0.974

0.041

0.040

1.485

8.07

0.43

0.000

− 0.003

M3: trait loading and intercept mi

612

55

154.88

80

1.94

0.982

0.977

0.039

0.040

1.522

10.71

0.22

0.000

− 0.002

M4: trait loading. intercept and state loading mi

612

47

165.02

88

1.88

0.982

0.978

0.038

0.044

1.561

11.19

0.19

0.000

− 0.001

IDENT

M1: no measurement invariance (mi)

612

56

49.20

34

1.45

0.994

0.988

0.027

0.032

1.316

    

M2: trait loading mi

612

50

65.99

40

1.65

0.990

0.983

0.033

0.051

1.310

17.04

0.01

− 0.004

0.006

M3: trait loading and intercept mi

612

44

84.92

46

1.85

0.985

0.978

0.037

0.055

1.372

16.83

0.01

− 0.005

0.004

M4: trait loading. intercept and state loading mi

612

38

95.85

52

1.84

0.983

0.978

0.037

0.060

1.438

10.97

0.09

− 0.002

0.000

INTRO

M1: no measurement invariance (mi)

612

56

154.56

34

4.55

0.901

0.808

0.076

0.072

1.367

    

M2: trait loading mi

612

50

161.45

40

4.04

0.900

0.835

0.070

0.074

1.365

6.65

0.35

− 0.001

− 0.006

M3: trait loading and intercept mi

612

44

167.76

46

3.65

0.900

0.857

0.066

0.075

1.394

8.53

0.20

0.000

− 0.004

M4: trait loading. intercept and state loading mi

612

38

157.48

52

3.03

0.913

0.890

0.058

0.075

1.340

− 24.89

1.00

0.013

− 0.008

EXTRI

M1: no measurement invariance (mi)

612

56

142.67

34

4.20

0.882

0.771

0.072

0.061

1.491

    

M2: trait loading mi

612

50

124.75

40

3.12

0.908

0.848

0.059

0.069

1.425

− 33.26

1.00

0.026

− 0.013

M3: trait loading and intercept mi

612

44

130.99

46

2.85

0.908

0.867

0.055

0.071

1.471

8.40

0.21

0.000

− 0.004

M4: trait loading. intercept and state loading mi

612

38

132.20

52

2.54

0.913

0.889

0.050

0.071

1.459

0.09

1.00

0.005

− 0.005

ACMOT

M1: no measurement invariance (mi)

779

56

47.52

34

1.40

0.991

0.982

0.023

0.034

1.214

    

M2: trait loading mi

779

50

57.90

40

1.45

0.988

0.980

0.024

0.045

1.239

10.18

0.12

− 0.003

0.001

M3: trait loading and intercept mi

779

44

79.40

46

1.73

0.978

0.968

0.031

0.055

1.251

20.70

0.00

− 0.010

0.007

M4: trait loading. intercept and state loading mi

779

38

85.21

52

1.64

0.978

0.972

0.029

0.056

1.259

6.03

0.42

0.000

− 0.002

ASELF

M1: no measurement invariance (mi)

779

95

339.81

157

2.16

0.954

0.938

0.039

0.051

1.236

    

M2: trait loading mi

779

89

397.26

163

2.44

0.941

0.924

0.043

0.069

1.270

39.20

0.00

− 0.013

0.004

M3: trait loading and intercept mi

779

77

457.42

175

2.61

0.929

0.914

0.046

0.068

1.303

52.18

0.00

− 0.012

0.003

M4: trait loading. intercept and state loading mi

779

65

454.67

187

2.43

0.932

0.924

0.043

0.067

1.282

− 13.66

1.00

0.003

− 0.003

  1. VALUE, Subjective test value; EFFOR, Effort. INTRI, Intrinsic regulation; IDENT, Identified regulation; INTRO, Introjected regulation; EXTRI, External regulation; ACMOT, Achievement motivation; ASELF, Academic self-concept. N, sample size; Par, number of estimated parameters. χ2, Chi square value; df, degrees of freedom; CFI, Comparative Fit Index; TLI, Tucker Lewis Index; RMSEA, Root Mean Square Error of Approximation; SRMR, Standardized Root Mean Square Residual. LLCorFac, Scaling Correction Factor for MLR; TRd, Satorra-Bentler scaled Chi square difference test
  2. *The current model (M) is compared to the previous model (M-1). Substantial losses in model fit (> − 0.01 CFI, > . 0.15 RMSEA) according to Chen (2007) are given in italics